The three representations of the generator of a stochastic CRN use the
three classes of random variables as bases: \({\sigma }_{{\rm n}}\)  (the
discrete indicator function on states, for the distribution
\({\rho }_{{\rm n}}\) ), \({{\rm n}}^{\underline{k}}\)  (discrete powers, for moments
\({\Phi }_k\) ), and \(z^{{\rm n}}\)  (continuous tilts, for the MGF \(\phi \!\left( z \right)\) ). The well-known direct
interconversions [1]}, [2]}, [3]}, [4]}
and the new one derived
in [5]}, [6]} facilitate
choosing bases with good convergence properties for different classes
of observables of interest. The connection among the three through
the large-deviations limit derived here, in addition to providing
approximation methods, shows connections of meaning across the
representations that are sometimes not apparent in their more
indirect, detailed interconversions.
